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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The Connes spectrum of group actions and group gradings for certain quotient rings
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by James Osterburg and Xue Yao PDF
Trans. Amer. Math. Soc. 347 (1995), 2263-2275 Request permission

Abstract:

Let $H$ be a finite-dimensional, semisimple Hopf algebra over an algebraically closed field $K$ where $H$ is either commutative or cocommutative. We let $A$ be an $H$-module algebra which is semiprime right Goldie. We show that the Connes spectrum of $H$ acting on $A$ is the Connes spectrum of $H$ acting on the classical quotient ring of $A$. In our last section, we define a symmetric quotient ring and show that the Connes spectrum of the ring and its quotient ring are the same. Finally, we apply our results to finite group actions and group gradings.
References
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Additional Information
  • © Copyright 1995 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 347 (1995), 2263-2275
  • MSC: Primary 16W30; Secondary 16S35, 16W50
  • DOI: https://doi.org/10.1090/S0002-9947-1995-1273514-5
  • MathSciNet review: 1273514